Finite Group DatabasebetaFinite Group Databasebeta| order | 11550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C52⋊C3×D77 |
| unambiguous semidirect product | C11⋊(D7×C52⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C11 | C2×C3 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
440 conjugacy classes — view the full character table.
| maximal subgroup of | #3874×D77, D77⋊#3874, D7×D11×C52⋊C3, … |
| maximal normal subgroup of | #3874×D77, D77⋊#3874, D7×D11×C52⋊C3, … |
| maximal quotient of | C52⋊C3×Dic77, C2×C52⋊C3×D77, D77×C52⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11550, 89);